TSTP Solution File: KLE027+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE027+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 02:21:50 EDT 2022
% Result : Theorem 0.81s 1.13s
% Output : Refutation 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE027+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jun 16 10:43:08 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.50/1.03 ============================== Prover9 ===============================
% 0.50/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.50/1.03 Process 387 was started by sandbox2 on n010.cluster.edu,
% 0.50/1.03 Thu Jun 16 10:43:09 2022
% 0.50/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32702_n010.cluster.edu".
% 0.50/1.03 ============================== end of head ===========================
% 0.50/1.03
% 0.50/1.03 ============================== INPUT =================================
% 0.50/1.03
% 0.50/1.03 % Reading from file /tmp/Prover9_32702_n010.cluster.edu
% 0.50/1.03
% 0.50/1.03 set(prolog_style_variables).
% 0.50/1.03 set(auto2).
% 0.50/1.03 % set(auto2) -> set(auto).
% 0.50/1.03 % set(auto) -> set(auto_inference).
% 0.50/1.03 % set(auto) -> set(auto_setup).
% 0.50/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.50/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.50/1.03 % set(auto) -> set(auto_limits).
% 0.50/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.50/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.50/1.03 % set(auto) -> set(auto_denials).
% 0.50/1.03 % set(auto) -> set(auto_process).
% 0.50/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.50/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.50/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.50/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.50/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.50/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.50/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.50/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.50/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.50/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.50/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.50/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.50/1.03 % set(auto2) -> assign(stats, some).
% 0.50/1.03 % set(auto2) -> clear(echo_input).
% 0.50/1.03 % set(auto2) -> set(quiet).
% 0.50/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.50/1.03 % set(auto2) -> clear(print_given).
% 0.50/1.03 assign(lrs_ticks,-1).
% 0.50/1.03 assign(sos_limit,10000).
% 0.50/1.03 assign(order,kbo).
% 0.50/1.03 set(lex_order_vars).
% 0.50/1.03 clear(print_given).
% 0.50/1.03
% 0.50/1.03 % formulas(sos). % not echoed (17 formulas)
% 0.50/1.03
% 0.50/1.03 ============================== end of input ==========================
% 0.50/1.03
% 0.50/1.03 % From the command line: assign(max_seconds, 300).
% 0.50/1.03
% 0.50/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.50/1.03
% 0.50/1.03 % Formulas that are not ordinary clauses:
% 0.50/1.03 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.03 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.03 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.03 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.03 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.03 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.03 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.03 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.03 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.03 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.03 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.03 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.03 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.03 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 17 -(all X0 all X1 all X2 all X3 all X4 (test(X3) & test(X4) -> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.13
% 0.81/1.13 ============================== end of process non-clausal formulas ===
% 0.81/1.13
% 0.81/1.13 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.13
% 0.81/1.13 ============================== PREDICATE ELIMINATION =================
% 0.81/1.13 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.81/1.13 19 test(c4) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.81/1.13 20 test(c5) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.81/1.13 21 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 0.81/1.13 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.81/1.13 Derived: complement(f1(c4),c4). [resolve(18,a,19,a)].
% 0.81/1.13 Derived: complement(f1(c5),c5). [resolve(18,a,20,a)].
% 0.81/1.13 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,21,a)].
% 0.81/1.13 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,22,a)].
% 0.81/1.13 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.81/1.13 Derived: c(c4) != A | complement(c4,A). [resolve(23,a,19,a)].
% 0.81/1.13 Derived: c(c5) != A | complement(c5,A). [resolve(23,a,20,a)].
% 0.81/1.13 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(23,a,21,a)].
% 0.81/1.13 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(23,a,22,a)].
% 0.81/1.13 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.81/1.13 Derived: c(c4) = A | -complement(c4,A). [resolve(24,a,19,a)].
% 0.81/1.13 Derived: c(c5) = A | -complement(c5,A). [resolve(24,a,20,a)].
% 0.81/1.13 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(24,a,21,a)].
% 0.81/1.13 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(24,a,22,a)].
% 0.81/1.13 25 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.81/1.13 26 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.81/1.13
% 0.81/1.13 ============================== end predicate elimination =============
% 0.81/1.13
% 0.81/1.13 Auto_denials: (non-Horn, no changes).
% 0.81/1.13
% 0.81/1.13 Term ordering decisions:
% 0.81/1.13 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. c4=1. c5=1. multiplication=1. addition=1. c=1. f1=1.
% 0.81/1.13
% 0.81/1.13 ============================== end of process initial clauses ========
% 0.81/1.13
% 0.81/1.13 ============================== CLAUSES FOR SEARCH ====================
% 0.81/1.13
% 0.81/1.13 ============================== end of clauses for search =============
% 0.81/1.13
% 0.81/1.13 ============================== SEARCH ================================
% 0.81/1.13
% 0.81/1.13 % Starting search at 0.01 seconds.
% 0.81/1.13
% 0.81/1.13 ============================== PROOF =================================
% 0.81/1.13 % SZS status Theorem
% 0.81/1.13 % SZS output start Refutation
% 0.81/1.13
% 0.81/1.13 % Proof 1 at 0.10 (+ 0.01) seconds.
% 0.81/1.13 % Length of proof is 39.
% 0.81/1.13 % Level of proof is 8.
% 0.81/1.13 % Maximum clause weight is 24.000.
% 0.81/1.13 % Given clauses 146.
% 0.81/1.13
% 0.81/1.13 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 17 -(all X0 all X1 all X2 all X3 all X4 (test(X3) & test(X4) -> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.13 19 test(c4) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.81/1.13 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.81/1.13 27 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.81/1.13 29 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.81/1.13 30 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.81/1.13 31 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 0.81/1.13 32 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 0.81/1.13 33 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.81/1.13 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 0.81/1.13 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.81/1.13 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 0.81/1.13 41 addition(multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2))),multiplication(c(c4),c3)) != addition(multiplication(c4,c1),multiplication(c(c4),c3)) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.81/1.13 42 addition(multiplication(c(c4),c3),multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2)))) != addition(multiplication(c4,c1),multiplication(c(c4),c3)). [copy(41),rewrite([33(15)])].
% 0.81/1.13 44 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.81/1.13 45 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.81/1.13 46 -complement(A,B) | addition(A,B) = one. [copy(45),rewrite([33(2)])].
% 0.81/1.13 53 c(c4) != A | complement(c4,A). [resolve(23,a,19,a)].
% 0.81/1.13 65 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(27(a,1),38(a,2,2)),rewrite([31(3),33(3)])].
% 0.81/1.13 85 complement(c4,c(c4)). [resolve(53,a,30,a(flip)),rewrite([30(5)])].
% 0.81/1.13 107 addition(c4,c(c4)) = one. [resolve(85,a,46,a)].
% 0.81/1.13 108 multiplication(c4,c(c4)) = zero. [resolve(85,a,44,a)].
% 0.81/1.13 229 multiplication(c4,multiplication(c(c4),A)) = zero. [para(108(a,1),36(a,1,1)),rewrite([32(2)]),flip(a)].
% 0.81/1.13 230 multiplication(c4,addition(A,c(c4))) = multiplication(c4,A). [para(108(a,1),38(a,1,1)),rewrite([65(4),33(6)]),flip(a)].
% 0.81/1.13 375 multiplication(c4,addition(A,multiplication(c(c4),B))) = multiplication(c4,A). [para(229(a,1),38(a,1,1)),rewrite([65(4),33(7)]),flip(a)].
% 0.81/1.13 379 addition(multiplication(c(c4),c3),multiplication(c4,multiplication(c4,c1))) != addition(multiplication(c4,c1),multiplication(c(c4),c3)). [back_rewrite(42),rewrite([375(14)])].
% 0.81/1.13 564 multiplication(c4,c4) = c4. [para(107(a,1),230(a,1,2)),rewrite([29(3)]),flip(a)].
% 0.81/1.13 569 multiplication(c4,multiplication(c4,A)) = multiplication(c4,A). [para(564(a,1),36(a,1,1)),flip(a)].
% 0.81/1.13 579 $F. [back_rewrite(379),rewrite([569(9),33(8)]),xx(a)].
% 0.81/1.13
% 0.81/1.13 % SZS output end Refutation
% 0.81/1.13 ============================== end of proof ==========================
% 0.81/1.13
% 0.81/1.13 ============================== STATISTICS ============================
% 0.81/1.13
% 0.81/1.13 Given=146. Generated=2400. Kept=546. proofs=1.
% 0.81/1.13 Usable=117. Sos=304. Demods=142. Limbo=10, Disabled=152. Hints=0.
% 0.81/1.13 Megabytes=0.63.
% 0.81/1.13 User_CPU=0.11, System_CPU=0.01, Wall_clock=0.
% 0.81/1.13
% 0.81/1.13 ============================== end of statistics =====================
% 0.81/1.13
% 0.81/1.13 ============================== end of search =========================
% 0.81/1.13
% 0.81/1.13 THEOREM PROVED
% 0.81/1.13 % SZS status Theorem
% 0.81/1.13
% 0.81/1.13 Exiting with 1 proof.
% 0.81/1.13
% 0.81/1.13 Process 387 exit (max_proofs) Thu Jun 16 10:43:09 2022
% 0.81/1.13 Prover9 interrupted
%------------------------------------------------------------------------------